Simulating the All-Order Hopping Expansion II: Wilson Fermions

Abstract

We investigate the extension of the Prokof'ev-Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the two-point function on a finite lattice to arbitrary order. Tests are conducted for a constant background field i. e. free fermions at some mass. For the method introduced here this is expected to be a representative case. Its advantage is that we know the exact answers and can thus make stringent tests on the numerics. The approach is formulated in both two and three space-time dimensions. In D=2 Wilson fermions enjoy special positivity properties and the simulation is similarly efficient as in the Ising model. In D=3 the method also works at sufficiently large mass, but there is a hard sign problem in the present formulation hindering us to take the continuum limit.

29 pages [12pt], 5 figures

References in corpus (12)

• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Worm algorithms for classical statistical models
• Monte Carlo errors with less errors
• The Loop Algorithm
• Meron-Cluster Solution of Fermion Sign Problems
• Chiral Limit of Strongly Coupled Lattice Gauge Theories
• Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo
• Efficient simulation of relativistic fermions via vertex models
• Cluster simulation of relativistic fermions in two space-time dimensions
• Loop representation for 2-D Wilson lattice fermions in a scalar background field
• Fermion loop simulation of the lattice Gross-Neveu model
• The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model

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• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
• Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
• Efficient simulation of relativistic fermions via vertex models
• Fermion bag solutions to some sign problems in four-fermion field theories
• A new dual representation for staggered lattice QCD
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions
• Geometric Algorithm for Abelian-Gauge Models
• Anomalous discrete chiral symmetry in the Gross-Neveu model and loop gas simulations
• The worm process for the Ising model is rapidly mixing
• Strong Coupling Lattice QCD in the Continuous Time Limit
• A factorization algorithm to compute Pfaffians
• Ising model as Wilson-Majorana Fermions
• Dual Non-Abelian Yang-Mills Simulations in Four Dimensions
• Fermion bag solutions to some sign problems in four-fermion field theories
• Leaf-excluded percolation in two and three dimensions
• A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at $\theta =\pi$